# Full text of "Analytical Mechanics"

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EQUILIBRIUM OF RIGID BODIES                   53
Substituting the given value of p in the expression for F we obtain
F = jjialpo C sinddB Jo
In order to determine p0 in terms of the total load on the bearings we make p satisfy the condition
Substituting the given value of p in the right-hand member of the preceding equation we have
— Trafoo
2P
or                                      pQ = —•
TraZ
Therefore                            ^ = — P
TT
and                              G = ~aP.
7T
It will be observed that the total frictional force varies with the load and is independent of the radius and of the length of the bearing; in other words it is independent of the area of contact.
PROBLEMS.
1.   Supposing the normal pressure to be the same at every point of the surfaces of contact, derive the expressions for the total frictional force and the resisting torque due to friction.
2.   Supposing the vertical  component of the total reaction at every point of the surfaces of contact to be constant, derive the expressions for the total frictional force and the resisting torque due to friction.
3.   Derive expressions for the total frictional force and the resisting torque upon the assumption that the normal pressure is given by the relation p = po sin2 0.
68.   Friction on Pivots. — The  problem  of friction  on pivots also is a problem of sliding friction.   The feature